Abstract
The digitisation \({\bf D}(R, (a, b))\) of a real disc \(D(R, (a,b))\) having radius \(R\) and centre \((a, b)\) consists of all integer points inside \(D(R, (a,b))\), i.e., \({\bf D}(R, (a,b)) = D(R, (a, b)) \cap {\bf Z}^2.\) In this paper we show that there are
different (up to translations) digitisations of discs having radius \(R\). More formally,
The result is of interest in the area of digital image processing because it describes how large the impact of the object position can be on its digitisation.
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Huxley, M., Zunic, J. Different Digitisations of Displaced Discs. Found Comput Math 6, 255–268 (2006). https://doi.org/10.1007/s10208-005-0177-y
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DOI: https://doi.org/10.1007/s10208-005-0177-y